A $5$ kg box slides down a $3-$m$-$high frictionless ramp and hits an identical $5$ kg box, which was initially stationary.

a$.[10$ pts$]$ If the boxes stick together, what is their velocity right after the collision?

b$.[10$ pts$]$ The ramp is very smooth, but the flat surface where the boxes slide after the collision is rougher. The coefficient of friction between the boxes and the rougher surface is $0\mathrm{.}3.$ How far do the $($stuck together$)$ boxes travel before stopping?